The Four Operations, Integers and Number Lines: Practice Questions

What is the absolute value of \( -25 + 10 \)?

Calculate the following:
\( (-2)^4 - (-3)^2 \)

A submarine is cruising at a depth of \( 250 \) m below sea level. It first descends a further \( 120 \) m and then ascends \( 85 \) m. What is its final position relative to sea level?

Evaluate the expression:
\( (-6) \times (-2) - 15 \)

Evaluate the expression:
\( (-3)^2 - 4 \times (-2) + (-5) \)

Calculate the value of \( (-4) \times 7 \div (-2) \).

Find the value of the integer \( k \) such that the expression \( [(-48) \div (-2)^3] - [k \times (-5)] \) equals \( 31 \).

Let \( x \) and \( y \) be two integers such that \( |x| = 8 \) and \( |y| = 5 \). Find the maximum possible value and the minimum possible value of the expression \( (x - y)^2 \).

Consider the following steps of calculation involving integers:
(a) Calculate the value of \( P \) if \( P = (-12) + 15 \div (-3) \).
(b) Calculate the value of \( Q \) if \( Q = (-4) \times [7 - (-2)] \).
(c) Using the values of \( P \) and \( Q \) found above, evaluate the expression \( 2P - Q \).

A sequence of numbers is defined by the following rule: the first term is \(-12\), and for any term \(n > 1\), the term is calculated by multiplying the previous term by \(-2\) and then subtracting \(15\).
(a) Find the second, third, and fourth terms of this sequence.
(b) Calculate the sum of the first four terms.
(c) Determine if the sum calculated in part (b) is a multiple of \(3\) and explain your reasoning using prime factorization.